Hotelling Rule Research Articles

Hotelling rule in non-renewable resources: A bibliometric and systematic literature review analysis

This research aimed to provide a comprehensive mapping of studies on the application of the Hotelling rule in non-renewable resources from 1970 to 2024, identifying the most prominent research topics and trends, key characteristics, evolution, and directions for future studies. To achieve this, the following research questions were addressed using a mixed-method approach, including bibliometric analysis, text mining, and content analysis: (i) How has research on the Hotelling rule in non-renewable resources evolved? (ii) What are the most relevant research topics and trends in Hotelling rule research? and (iii) What future directions should studies on the Hotelling rule in non-renewable resources pursue? A total of 197 journal articles extracted from the Scopus database were analyzed to map the main body of literature. Four main research clusters were identified: (1) theoretical and empirical perspectives on the Hotelling rule, (2) the Hotelling rule in non-renewable resource management, (3) economic policy and sustainability within the Hotelling framework, and (4) resource depletion and pricing under the Hotelling rule. Four key areas for future research were proposed, focusing on diversification to other non-renewable resources, evaluation of policies and geographical contexts, technological innovations and government policies, and sector-specific applications of the Hotelling rule. These directions are crucial for promoting sustainability in the management of non-renewable resources over time.

Dynamic efficiency of tradable license system with time-flexible quantities

Tradable license system (TLS) is a fundamental policy instrument for environmental management or resource development. We construct a muti-periods dynamic model with respect to a general TLS with three time-flexible quantity mechanisms: fixed quantity, solely banking, and banking and borrowing, in which the firm maximizes its discounted net benefits over the horizon by selecting an optimal license usage by license trading across agents or transferring across periods. The dynamic efficiency performance and price dynamics in TLS are respectively examined. The decentralized equilibrium in TLS with fixed quantity cannot achieve benefit-maximum unless initial license allocation is efficient. The decentralized behaviors in TLS with solely banking lead to benefit-maximum and price dynamics follows the Hotelling rule, if and only if the cumulative initial license allocation in each period is not less than the optimum, while TLS with banking and borrowing can achieve the optimal outcome and price dynamics follows Hotelling rule regardless of the initial allocation. The findings highlight the synergistic effects between the initial allocation of licenses and time-flexible quantity mechanisms in TLS design.

Do supercycles dominate commodity price movements?

This study utilizes a frequency domain approach to decompose the prices of 21 primary commodities into transitory, supercycle, and permanent components from 1900 to 2022. The results reveal the presence of four heterogenous supercycles, with an average duration of 24 years. These cycles, however, contribute only modestly to price variability while the permanent component contributes the most. The paper also shows that different commodities are consistent with various theories of price movements, including Engel's law, Hotelling's rule, and Schumpeter's cyclicality (or Kondratieff's waves).

Non-Renewable Resources and Sustainable Resource Extraction: An Empirical Test of the Hotelling Rule’s Significance to Gold Extraction in South Africa

The study sought to test the applicability of Hotelling’s rule to gold extraction in South Africa. In environmental economics, Hotelling’s rule has come to be a pillar of the exhaustible resources framework and in addition to this, it has presented essential insights into the consumption and extraction of non-renewable resources. According to Hotelling’s Rule, the extraction path in competitive market economies will, under certain circumstances, be socially optimal. An extraction path that is not socially optimal compromises the welfare of future generations. The welfare of South Africa’s present population, particularly in the future, will be greatly determined by the stock of natural resources available. Currently, the production processes deplete natural resources in a way that is not sustainable. For instance, South Africa’s gold reserves are becoming depleted at a rate that, within 25 to 33 years, will mean the end of the industry on which South Africa’s economy has been built. This raises questions regarding how much of these non-renewable resources (gold) should be extracted today, and how much should be saved for future use or for future generations. Is gold being depleted more rapidly than the optimisation level suggested by Hotelling’s Rule? In order to empirically test Hotelling’s Rule, the study was guided by previous literature that had sought to test it, namely, the previously used graphical analysis and autoregressive distributed lag (ARDL) approach to assess the applicability of Hotelling’s Rule. The results showed that there seems to be no significant relationship between interest rates and gold processes. This shows that Hotelling’s Rule does not hold in South Africa. The results of the study suggested that the gold extraction in South Africa is not following a social optimal path. The study recommended that the government come up with measures that prolong the lifespan of the gold reserves. These included research and development to promote technological innovations in the mining sector.

The Impact of Socio-Economic Inertia and Restrictions on Net-Negative Emissions on Cost-Effective Carbon Price Pathways

Many countries have indicated to plan or consider the use of carbon pricing. Model-based scenarios are used to inform policymakers about emissions pathways and cost-effective carbon prices. Many of these scenarios are based on the Hotelling rule, assuming that a carbon price path increasing with the interest rate leads to a cost-effective strategy. We test the robustness of this rule by using experiments with plausible assumptions for learning by doing, inertia in reducing emissions, and restrictions on net-negative emissions. Analytically, we show that if mitigation technologies become cheaper if their capacities are increased, Hotelling does not always apply anymore. Moreover, the initial carbon price is heavily influenced by restrictions on net-negative emissions and the pathway by both restrictions on net-negative emissions and socio-economic inertia. This means that Hotelling pathways are not necessarily optimal: in fact, combining learning by doing and the above restrictions leads to initial carbon prices that are more than twice as high as a Hotelling pathway and thus to much earlier emission reductions. The optimal price path also increases less strongly and may even decline later in the century, leading to higher initial abatement costs but much lower long-term costs.

Genuine Savings and Sustainability with Resource Diffusion

We consider a spatial extension of genuine savings and wealth as a capital-based indicator of sustainability. In both inefficient and efficient economies, where well-being is locally or globally maximized, respectively, the well-known Hotelling rule and Hartwick (Dixit–Hammond–Hoel) investment rules and results are extended, depending on the extent of the spatial diffusion of natural capital. It is shown that the net present value of any future change in neighboring resource stocks affects the current change in intergenerational well-being. Numerical examples show the relevance of such parameters as the diffusion rate, discount rate, and marginal utility of consumption. Moreover, they suggest the exact adjustments to be made in aggregating or disaggregating the sustainability of different spatial units, which is not addressed in the current practice of green or wealth accounting.

Market Power, Intertemporal Permits Trading, and Economic Efficiency

The banking and borrowing (BB) system has been developed gradually in the tradable permits market to perform a role as an environmental management tool. One question naturally arises as to how it will impact the behaviors of firms and the efficiency in presence of market power in the permits market. This paper considers market power in two cases: with and without the BB system. The equilibrium behaviors of the firms are identified in two cases. The findings show that the producing and discharging behaviors of firms depend on the permits price elasticity of output price without BB system, while they only depend on the growth rate of the output price in the BB system. Although both cases fail to obtain efficient solutions, the market with a BB system is capable of alleviating the inefficiency arising from market power compared with that without a BB system. The path of permits price satisfies the Hotelling rule in the case of the BB system, while it is closely related to the path of output price and output price elasticity of permits price in the case without the BB system.

Exhaustible Resources and Classical Theory

Smith, Ricardo, Marx and Sraffa made no theoretical distinction between exhaustible resources and lands. The very notion of exhaustibility, however, can be opposed to that of “indestructible powers of the soil” (Ricardo) and calls for a specific analysis distinct from that of rent. The diversity of the contemporary attempts to deal with that question in a Classical framework shows how varied are the understandings of the main methodological features of Classical theory. Three crucial points emerge: first, the treatment of prices, which are invariant in classical theory but, according to the Hotelling rule, are changing through time for exhaustible resources; second, the notion and the measure of the rate of profits; and, third, the relationship between economic analysis and a more historical and sociological approach stressing the balances of power between classes. Our own approach starts from a very simple model, called the corn-guano model, where guano is the exhaustible resource, and examines the dynamics of such an economy on the physical side and the value side. These lessons serve as a basis for an extension to multisector models. We provide a critical assessment of a few alternative approaches developed by Sraffian scholars.

Non-Renewable Resource Economics and Geological Constraints: a Review

In 1931, Harold Hotelling introduced the Hotelling rule—the fundamental theoretical principle of non-renewable resource economics. However, almost ninety years later, economists are still unable to establish a generalized, empirical validity for the rule. As concerns mineral resources, recent developments suggest that geological constraints may play a larger role in explaining why they would not follow the rule, than the traditional understanding. This paper reviews the evolving role geological constraints have played in the literature on non-renewable resource economics. It explores their evolution from the early days, where the focus was on the exhaustibility constraint as the main determinant of the evolution of price and output, to more recent years, with the realization that geological constraints can be a promising route to explain empirically accepted stylized facts.

The Hotelling rule in non‐renewable resource economics: A reassessment

AbstractHarold Hotelling's 1931 contribution is known for providing a basic principle—the Hotelling rule—to the economics of non‐renewable resources. Nearly 90 years later, empirical tests conclude the rule lacks empirical validity, requiring strong amendments to describe the long‐term, aggregate behaviour of its target object. On the basis of Hotelling's unpublished archival material, this paper revisits the place given to the Hotelling rule in non‐renewable resource economics. Our reconstruction shows that Hotelling's 1931 paper has been misinterpreted: from the outset, the Hotelling rule was not valid for mineral resources. In contrast, the consideration of two inherent geological constraints, alongside exhaustibility, offered the opportunity for an alternative basic framework, capable to generate bell‐shaped and U‐shaped equilibrium trajectories for supplies and prices, respectively. Inspired by this unknown aspect of Hotelling's work brought to light by our archival investigation, we sketch this alternative basic model, enabling non‐renewable resource economics to circumvent the empirical shortfalls of the Hotelling rule.

Adverse selection, commitment and exhaustible resource taxation

This paper studies the contractual relationship between a government and a firm in charge of the extraction of an exhaustible resource. Governments design taxation scheme to capture resource rent and they usually propose contracts with limited duration and possess less information on resources than the extractive firms do. This article investigates how information asymmetry on costs and an inability to commit to long-term contracts affect tax revenue and the extraction path. This study gives several unconventional results. First, when information asymmetry exists, the inability to commit does not necessarily lower tax revenues. Second, under asymmetric information without commitment, an efficient firm may produce during the first period more or less than under symmetric information. Hence, the inability to commit has an ambiguous effect on the exhaustion date. Third, the modified Hotelling's rule is such that an increase in the discount factor does not necessarily reduce the first-period extraction.

Hotelling Meets Crypto-Currency: Do Bitcoin Rents Follow Hotelling's Rule?

Hotelling's Rule of non-renewable resource extraction was first proposed in 1931, but strong empirical evidence supporting Hotelling's predictions has been elusive. Recognizing the complications in natural resource markets, we test Hotelling's Rule using bitcoin rents. Bitcoin is similar to natural resources in that new coins enter the market solely through the efforts of individual agents expending computer resources to attain bitcoins, which can then be sold on exchanges for profit. Bitcoin has a fixed and known resource stock, can be accessed by anyone with a computer, exhibits a fairly homogeneous and easily modeled mining'' technology, and extraction rates follow restricted and pre-determined patterns. Aspects of capital investment and mining returns are observable and can be tracked over time, making bitcoin an ideal test bed for Hotelling's Rule. We calculate the growth rate of the net asset price of Bitcoin, and compare it to the growth rate of several market indicies (GSPC, HYG) over the same time period. We test for and find evidence of a co-integrating relationship, providing support for Hotelling's rule in that any deviations from the theoretical price path bring economic forces to bear that restore the proper pricing relationship.

How Does the EU ETS Reform Impact Allowance Prices? The Role of Myopia, Hedging Requirements and the Hotelling Rule

How Does the EU ETS Reform Impact Allowance Prices? The Role of Myopia, Hedging Requirements and the Hotelling Rule

Sustainable Energy Delivery for Africa’s Changing Climate: An Economic Assessment

This paper assesses Africa’s energy future in a changing global climate to inform development policy. In the midst of economic and energy challenges, coupled with COVID-19 pandemic recovery, Africa is expected to meet global climate obligations. While it makes sense to develop climate resilient economies, Africa appears stuck in its pre-climate change energy delivery systems. The economic, social and environmental consequences of this stagnation are suboptimal for the continent, calling for urgent transition to more sustainable energy delivery. The study analyzed fossil fuel use in Africa from 1960 to 2016, based on a modified Hotelling Rule. Through time series data, the sustainable marginal cost of energy for Africa was estimated. The study further derived the optimal point in time when Africa should switch from fossil fuels as a main source of electricity generation to renewable energy, due to climate change. The study finds more than 70 percent increase in the marginal cost of fossil fuel compared to a cumulative reduction of 80 percent in the marginal cost of solar photovoltaic over the study period. Also, the switch point to renewable energy as the main source of electricity in Africa was found to be 2003. For sustainable delivery of energy in Africa, the study recommends policies to internalize the externalities of fossil fuel, backed by recovery subsidies to make up for the loss of welfare from fossil fuel use, and to create an enabling environment for a speedy energy transition in Africa’s changing climate.

The reformed EU ETS - Intertemporal emission trading with restricted banking

With the increase of the linear reduction factor, the implementation of the market stability reserve and the introduction of the cancellation mechanism, the EU ETS changed fundamentally. We develop a discrete time model of the intertemporal allowance market that accurately depicts these reforms assuming that prices develop with the Hotelling rule as long as the aggregated bank is non-empty. A sensitivity analysis ensures the robustness of the model results regarding its input parameters. The accurate modelling of the EU ETS allows for a decomposition of the effects of the individual amendments and the evaluation of their cost effectiveness. The market stability reserve shifts emissions to the future but is allowance preserving. A one-time cancellation reduces the overall emission cap, increasing allowance prices in the long run, but does not significantly impact the emission and price path in the short run. The increased linear reduction factor leads with 9 billion cancelled allowances to a stronger reduction than the cancellation mechanism and is therefore the main price driver of the reform.

The Social Cost of Sub-Soil Resource Use

This paper presents a market-price-based method to value sub-soil resources in environmental Cost-Benefit Analysis and Life Cycle Assessment. The market price incorporates the privileged information of the market agents, explicitly or implicitly anticipating future applications of the resource, future backstop technologies, recycling potentials, the evolution of reserves and extraction costs. The market price is therefore considered as the best available integrated information reflecting the actual values of these parameters. Our method is based on the Hotelling rule and the fact that private agents discount future costs and benefits at a higher rate than society as a whole. In practice, the price of the last resource unit sold is calculated with the Hotelling rule using a market discount rate. Then, the price at depletion is retropolated with a social discount rate smaller than the market discount rate. The resulting corrected “socially optimal” price is higher than the market price. The method allows to calculate the social cost of resource exhaustion, which is applicable in Cost-Benefit Analysis and Life Cycle Assessment. The method is applied to mineral and fossil resources and the results are compared with other recent methods that seek to place a monetary value on resource depletion.

Is Recycling a Threat or an Opportunity for the Extractor of an Exhaustible Resource?

We examine the best extraction strategies for the provider of an exhaustible resource that can be recycled. In a two-period model of resource extraction, the extractor faces prospective entry by a recycler that incurs a fixed cost to produce a perfect substitute of the virgin resource. Its entry is an opportunity or a threat for the extractor, depending on whether it maximizes social welfare or its own revenue. Our results highlight how prospective recycling modifies the Hotelling rule. We characterize various entry possibilities. The benevolent extractor may accommodate or promote recycling, while the self-interested extractor may accommodate or deter recycling.

Sustainability with endogenous discounting when utility depends on consumption and amenities

We study the issue of sustainability using a model with a stock of man-made capital and a stock of exhaustible natural resource that provides a flow of amenity services as well as an input for the production of a consumption good. We ask under what conditions the utility flow will be a constant if infinitesimal households discount their utility using an endogenous utility discount rate that depends some macroeconomic variables. Our main result is that for the utility flow to be constant, the utility discount function must be the marginal product of capital function adjusted for the growth rate of aggregate consumption weighted by the elasticity of the consumer’s marginal rate of substitution between the final good and the amenity services. We demonstrate that Hartwick’s Rule holds but the Hotelling Rule must be modified. We also provide an explicit analytical example to confirm the general result.

Nonrenewable Resources, Strategic Behavior and the Hotelling Rule: An Experiment

We use a laboratory experiment to investigate a novel reason for the lack of empirical support for the Hotelling rule for nonrenewable resources. Specifically, we test whether producers with large resource stocks focus less on the dynamic component of their extraction decision, making them shift extraction to the present and focus more on strategic behavior. Exploiting exogenous variation in stock size in a nonrenewable resource duopoly laboratory experiment, we find that producers with large stocks indeed pay significantly less attention to dynamic optimization, and shift extraction to the present, leading them to overproduce relative to the Hotelling rule.

Extracting information or resource? The Hotelling rule revisited under asymmetric information

AbstractA concessionaire has private information on the initial stock of resource. A “virtual Hotelling rule” describes how the resource price evolves over time and how extraction costs are compounded with information costs along the optimal extraction path. Fields which are heterogeneous in terms of their initial stocks follow different extraction paths. Resource might be left unexploited in the long run as a way to foster incentives. The optimal contract may sometimes be implemented through royalties and license fees. With a market of concessionaires, asymmetric information leads to a “virtual Herfindahl principle” and to another form of heterogeneity across active concessionaires.